Universal scaling in first-order phase transitions mixed with nucleation and growth

TL;DR

This paper demonstrates that universal hysteresis scaling predicted by renormalization-group theory can be observed in first-order phase transitions when combined with nucleation and growth theories, unifying the understanding of phase transition types.

Contribution

It provides numerical evidence that integrates renormalization-group theory with nucleation and growth in FOPTs, unifying the treatment of first-order and continuous phase transitions.

Findings

Universal hysteresis scaling emerges in FOPTs when combined with nucleation theories.

The approach unifies the theoretical framework for different classes of phase transitions.

Numerical simulations in the 2D Ising model support the proposed theory.

Abstract

Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only qualitatively accounted for by classical theories of nucleation, since their predictions often disagree with experiments by orders of magnitude. A theory to integrate FOPTs into the framework of the renormalization-group theory has been proposed but seems to contradict with extant wisdom and lacks numerical evidence. Here we show that universal hysteresis scaling as predicted by the renormalization-group theory emerges unambiguously when the theory is combined intimately with the theory of nucleation and growth in the FOPTs of the paradigmatic two-dimensional Ising model driven by a linearly varying externally applied field below its critical point. This not only provides a new method to rectify the nucleation theories, but also unifies the theories for both classes of transitions and FOPTs can be studied using universality and scaling similar to their continuous counterpart.